Below are a bunch of questions (list will be complete by Friday afternoon) that can serve as a study guide for the final.

The final itself will be constructed from a subset of these very questions or questions very similar to these.

Be prepared to graph data on the final. Graph paper will be provided.

Relevant Formulae:

1. Kinetic Energy = 1/2mv²
2. Potential Energy = mgh
3. F = ma
4. V_av = 1/2(v_i + v_f) Questions:
5. distance = average velocity x time
6. distance = 1/2gt²
7. velocity = acceleration x time
8. angular momentum = mwr
9. linear velocity = rw
10. momentum = mass x velocity
11. V_x = V cosineq
12. V_y = V sineq
13. FDt = mDV
14. Pressure = Force/area
15. Pressure + rgh + 1/2rv² = Constant

Notes on Units:

• Mass is measured in kilograms (kg)
• Length is measured in meters (m)
• Time is measured in seconds (s)
• Force is measured in Newtons (N)
• Energy is measured in Joules (J)
• Pressure is measured in Pascals (pa)
• Power is measured in Watts (W)

Relevant Constants:

• g = 9.8 m sec^-2 (which you can round to 10)
• cosine 45 = sine 45 = .707 (1 over the square root of 2)
• cosine 60 = 1/2; sine 60 = .86
• cosine 30 = .86; sine 30 = 1/2
• cosine 0 = 1; sine 0 = 0

Questions

1. Here is some data:

   
   X      Y       Time
   
   10    10       1 second
   12    15       2 seconds
   8     18       3 seconds
   10    20       4 seconds
   10    25       5 seconds
   15    26       6 seconds
   17    32       7 seconds
   15    15       8 seconds
   10    12       9 seconds
   10     5      10 seconds
   

   Plot up the time sequence in the X-y Plane.

   • In which time period was the average velocity in the X direction the greatest?
   • In which time period was the average velocity in the Y direction the greatest?
   • In which time period was the total velocity the greatest?

2. A car moves along a frictionless track with a horizontal acceleration of 4 centimeters sec ^-2. The cart has an initial velocity of 10 centimeters per second and an initial position of x = 0 cm.
   • What will the velocity of the cart be after 5 seconds?
   • What is the total distance traveled after 5 seconds.

3. You drop a ball from a height of 20 meters. What will the impact velocity be?

4. You decide to drive to LA. Why not. During the first 4 hours your velocity is constant at 80 miles per hour. During the next 2 hours your velocity is constant at 60 mph. During the last 6 hours your velocity is constant at 70 mph. What was your total distance traveled?

5. I toss a ball into the air with an initial velocity of 10 m/sec. What is the average velocity of the ball during the time it rises to its maximum height?

6. Explain why momentum can be considered as a vector quantity.

7. Explain why energy is not a vector quantity?

8. Formulae 11 is known as what in physics?

9. Demonstrate that you can express pressure as
   P = rgh where r = density.

10. Power is defined as the rate at which energy is used or Energy/time; Show that Power can be expressed as force x velocity.

11. 

    A ball suffers a collision with the wall as shown in the figure. The ball has a velocity, V. What are the X and Y components of the velocity of the ball before the collision?
    What is the magnitude of the change in momentum of the ball, if the speed of the ball has the same value before and after the collision?

12. A 50 kg cyclist travels on a level road at a steady 6 ms-1 (relative to the road) into a head wind of 15 ms-1. The forces opposing the cyclist's motion are air resistance (65 N) and tyre rolling friction (15 N). What is the power output of the cyclist (in kW)?

13. Draw a sketch of a block on an inclined plane and draw a vector which represents a) the gravitational force and b) the frictional force. (hint: look at the Lab 4 applet)

14. I throw a ball into the air with an initial velocity of 3 m/s. How high will the ball rise? How long will it take to return to my hand?

15. Explain how Newton's first law assists us in getting to the Moon.

16. What is the potential energy in a 10 kg mass suspended at a height of 100 meters above the surface of the earth?

17. If we drop that mass, and assume no energy loss, what will the impact velocity be?

18. A force of 300 Newtons is applied to a 10 kg object. What will its acceleration be?

19. Explain the physical process that creates pressure inside an inflated balloon.

20. What happens to particles when they are at a temperature of Absolute Zero?

21. A 1 kg bullet is fired at a velocity of 1000 meters/second. The bullet strikes a wooden cart of mass 100 kg that is on a frictionless track. What is the velocity of the cart after the bullet strikes it?

22. Plot the position vs time graph for an object subject to the following conditions:
    • it starts at x=+4 cm and zero velocity
    • at 4 seconds the object is at x =+13 cm
    • at 6 seconds the object is at x =+10 cm
    • at 8 seconds the object is at x =+10 cm
    • at 8 seconds the object is subject to a constant acceleration of 4 meters per second²

23. What will be the x position of this object at t = 10 seconds?

24. Explain why the pressure of a gas depends on its temperature

25. Explain why the pressure of a gas depends on its density.

26. What is Bernoulli's Principle?

27. Why doesn't the Sun collapse into a black hole?

28. Explain how a curveball works

29. Show that pressure can be expressed as Energy per unit Volume.

30. Write down an expression for Newton's second law that involves momentum

31. What is an impulse?

32. What is the concept of thermodynamic equilibrium?

33. Explain how a heat engine works. What is the efficiency of a heat engine operating between reservoirs of T= 50 degrees C and T = 100 degrees C.

34. Explain how conservation of momentum helps us to detect Jupiter size planets around nearby stars.

35. Explain why the moon is getting farther from the earth

36. How is angular momentum analogous to linear momentum? What is the analog of mass in rotational dynamics?

37. From Newton's third law, derive an expression for the acceleration of the earth that is produced by your mass.

38. Particle one has a mass of 2 kg and velocity of 10 m/s. Particle two has a mass of 4 kg and a velocity of 5 m/s. The two particles collide and stick. What is the velocity of the stuck particles? How much kinetic energy was lost during the collision?

39. What is the difference between in elastic and inelastic collision? Which type is most common in the macroscopic world?

40. Explain how Newton's Second Laws in combination with Newton's Law of Gravitation can be used to measure the Mass of the earth.

41. What determines your weight?

42. I have a cannon that shoots a cannon ball at a 45 degree angle with a velocity of 100 meters/sec. Ignoring air friction, how far will the shoot go?
43. What as the time of flight of the cannonball?

44. If I change the cannon angle to 60 degrees, how high will the cannonball go?

45. If I increase the distance between two objects of mass, M, by a factor of two, how much will the gravitational force decrease by?

46. Give a physical definition of mass

47. Show in a velocity vs time plot, how you would detect a change in the acceleration of an object.

48. If a force acts on an object, what happens to that object

49. Explain what a systematic error is

50. Explain what a random error is and how it occurs. Is there anyway to eliminate random error?

51. Concisely state what the law of energy conservation is

52. Explain why it would be a violation of Energy conservation if different masses fell at different rates in a gravitational field.

53. Using Newton's second law, explain why low mass cars get better fuel economy than high mass cars.

54. How does friction manifest itself as a force?

55. Explain the shoot the monkey demonstration. Why is it that Garfield was always hit by the dart?

56. A truck is moving at a constant velocity of 50 meters/second. Your in the back of a truck with a friend, a small friend. You throw your friend straight up into the air with a velocity of 10 meters/second. Immediately after you have thrown your friend into the air, the truck slows down to 40 meters/second. What is the approximate x-position of the truck and your friend when your friend hits the ground.?

57. Why, in projectile motion, does an angle of 30 degrees have the same range as an angle of 60 degrees?

58. How does energy conservation help to determine total range and maximum height of a projectile?

59. What is the kinetic energy of a 1000 kg car moving at 10 m/s. How high could a 25 kg bag of sand be thrown vertically using this much energy?

60. A car of mass 1000 kg is moving at 20 m/s, what is its momentum? The driver steps lightly on the break for 10 s and slows the car with constant deceleration down to 10 m/s. What is the momentum after the car slows down? What was the force acting on the car during the 10 s?

61. If a rocket ship starting from rest accelerates at a rate of 10 m/s² for a period of 100 days. What is its final velocity and how far did it travel in the 100 days?

62. Bob is driving along a highway and at 9:00am Bob is driving at 100 km/hr. During the next two hours he accelerates steadily and at 11:00 he is driving at 140 km/hr. How far did he travel during the two hour period between 9:00 and 11:00?

63. A car moving at 5 km/hr collides with two stationary cars of identical mass which are in neutral. If the collision is totally elastic what will happen afterwards. Which two conservation laws apply here?

64. You swing a toy stuffed lion around your head when the string breaks. Sketch the subsequent motion of the lion as seen from above. Explain your sketch in terms of the applicable Newton's laws.

65. If you push a block across level ground at a constant velocity by exerting a force of 200 N, what is the net force acting on it? Are you doing any work? If so, what becomes of the energy of the work. How much work do you do if you move the block 2 m?

66. A professor holds a very heavy pendulum bob (a bowling ball) up to his nose and releases it. He bravely waits with his head jammed up against the blackboard, for the ball to swing back and crush his skull. The belief in which conservation law allows him to wait so bravely? Explain how it applies here.

67. A rubber ball is released from a height of 10 m. It bounces off the grass and rebounds to a maximum height of 5 m. Did the ball have more or less energy after the bounce? Explain your answer in terms of conservation of energy.

68. A car with mass 1500 kg is in neutral (i.e. so the the wheels are free to turn without friction) and at rest on a level road. Linda can push it with a force of 300 N. How long does it take her to get it moving at a speed of 2 m/s assuming that there is no friction or drag.

69. Explain why a force is apparently exerted on an object when it is in uniform circular motion.

70. A dog running at a constant 12 ms-1 is initially 30 m behind a rabbit racing for dear life at 9 ms-1. After what time will the dog catch up with the rabbit (in seconds)?

71. The gauge pressure in the enclosed container A is P_a = 10 000 pascals. Fluid A has a density = 1200 kg m-3 and the height of fluid A is h_A = 5 m. Fluid A is in contact with Fluid B (see figure). If tube B is open to the atmosphere and the density of fluid B is = 1000 kg m-3, then the height to which fluid B rises is (in m). (Hint: refer to Bernoulli's equation above).

72. 4 kg container has a velocity of 3 ms-1 after sliding 2 m down a ramp with a slope at 30 degrees to the horizontal. The container starts from rest.
    • What is the average velocity of the container?
    • How long did it take to slide down a distance of 2 meters?
    • What is the approximate acceleration of the container>
    • What is the total force on the container?
    • What is the force on the container in the direction of its motion?
    • What is the frictional force that is opposing the motion?

73. I throw a ball into the air and it reaches a height of 60 meters. Ignore air resistance. What was the initial velocity of the ball?

74. A 0.25 kg ball is dropped from a height of 1 m. It rebounds to a height of 0.75 m.
    a.How much energy is lost in the collision with the ground?
    b) If the ground exerts an average force of 300 N on the ball, find the time for which the ball is in contact with the ground.
    c) Draw a graph of the velocity of the ball against time. (Show a scale on both axes of the graph.)

75. the pressure in a sealed container is 13lbs/in^2 at 32 degrees Fahrenheit (ice water) and 18lbs/in^2 at 212 degrees Fahrenheit (boiling water) At what temperature on the Fahrenheit scale is Absolute Zero?

76. A skier of mass 70 kg starts from rest at the top of a hill and reaches the bottom of the hill with a speed of 10 ms-1. The vertical height of the hill is 20 m. How much work is done on the skier by the forces of friction (in joules)?

77. A 60 kg athlete runs with a constant velocity of 2 ms-1 over a distance of 100 m along an upward sloping ramp. The velocity in the y direction is 1 m/s.
    a) what is the slope of the ramp?
    b) What is the potential energy of the athlete after they have run 100 meters?

78. Which of the four points is under the lowest pressure? Which two points are at equal pressure? Is the pressure at point 3 greater or less than at point 1?

79. If you hold a piece of wood 10 meters from the surface of the earth and drop it, describe how the energy is converted from one form to another during the process of falling. What happens to this energy when the wood strikes the ground? (10 pts)

80. Explain why the frictional force does not depend upon the contact area between an object and a surface.

81. Your on a planet with a gravitational acceleration of 20 m/sec^2? How far will you fall in 2 seconds?

82. Which has more momentum, a 100 kg object moving at 1 kilometer per second or a 1000 kg object in a circular orbit with a radius of 100 meters and an orbital period of 100 seconds?